Dmitry K. Gridnev
Published 2012-08-23, updated 2012-08-27Version 2
For a sequence of self--adjoint operators, which converges in the norm resolvent sense, the formula is derived, which expresses the essential spectrum of the limit through the essential spectrum of the elements of the sequence.
Comments: The paper has been withdrawn due to a wrong example concerning compact operators. Furthermore, the proof in Weidmann's back appears to be correct. With thanks to F. Gesztesy and Gerhard Teschl
Analytic description of the essential spectrum of a family of $3 \times 3$ operator matrices
The Faddeev Equation and Essential Spectrum of a Hamiltonian in Fock Space
On Eigenvalues Problem for Self-adjoint Operators with Singular Perturbations
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